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Pythagorean Identities

Trigonometric identities bring new life to the Pythagorean theorem by re-envisioning the legs of a right triangle as sine and cosine. See more

Derivation

The diagram above implies \( a^2 + o^2 = h^2 \). What Pythagorean identity is derived when both sides of the equal sign are divided by \( o^2 \)?

Which of these equations cannot be derived from the others?

Which of the following is equivalent to \( r ?\)

Which identity is directly implied by applying the Pythagorean Theorem to triangle \(ABC?\)

Remember: the Pythagorean Theorem says that \(AB^2 + BC^2 = AC^2.\)

Which identity can be obtained by dividing both sides of \( \sin^2(\theta) + \cos^2(\theta) = 1 \) by \( \cos^2(\theta) ?\)

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